We investigate spreading and recovery of disease in a square lattice, and, in particular, emphasize the role of the initial distribution of infected patches in the network on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, viz., infected core patches (ICP), infected peripheral patches (IPP), and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration; however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue-based semianalytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.

中文翻译：

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感染在正方形格子中扩散和恢复

我们研究方格中疾病的传播和恢复，特别是强调网络中感染斑块的初始分布对地方性疾病进展和恢复过程（如果有）的迁移（如果有）启动的作用。易感主机和受感染主机。该疾病以感染和无感染部位的三种可能的初始分布模式开始，即。，受感染的核心补丁（ICP），受感染的外围补丁（IPP）和随机分布的受感染补丁（RDIP）。我们的结果表明，随着迁移的增加，感染在晶格中单调扩散，而在ICP病例中未显示任何恢复迹象。在国际植检门户网站的情况下，随着迁移的增加，其遵循类似的单调发展。但是，自组织的愈合过程开始于更高的迁移，导致晶格以临界迁移率完全恢复。令人鼓舞的是，对于最初的RDIP安排，临界迁移率较低的情况下，恢复的机会要高得多。进行了基于特征值的半分析研究，以确定实现稳定的无感染晶格的临界迁移速率。感染斑块的初始部分和感染力在自组织恢复中起重要作用。对于RDIP案件，他们遵循决定恢复过程的指数律。对于ICP安排令人沮丧的情况，我们提出了晶格中链路的随机重新布线，允许长距离迁移路径有效启动恢复过程。因此，随着遵循严重迁移的幂定律的重新布线概率，全球感染的流行率下降并逐步提高，并导致诞生了无感染的紧急网络。我们建议随机重排网格中的链接，以允许长距离迁移路径有效启动恢复过程。因此，随着遵循严重迁移的幂定律的重新布线概率，全球感染的流行率下降并逐步提高，并导致无感染网络的诞生。我们建议随机重排网格中的链接，以允许长距离迁移路径有效启动恢复过程。因此，随着遵循严重迁移的幂定律的重新布线概率，全球感染的流行率下降并逐步提高，并导致无感染网络的诞生。